Kuta Software - Infinite Calculus
Name_
Differentiation - Logs and Exponentials
Date_ Period_
Differentiate each function with respect to x.
1) y = 4
4x4
2) y = 4
3) y = log 3 3 x 2
5) y = log 3 (3 x 5 + 5)
7) y = (4 + 2)
x3
9) y = 3
5 x 3
4) y = log 2 4
Kuta Software - Infinite Calculus
Name_
Differentiation - Trigonometric Functions
Date_ Period_
Differentiate each function with respect to x.
1) f ( x) = sin 2 x 3
2) y = tan 5 x 3
3) y = sec 4 x 5
4) y = csc 5 x 5
5) y = (2 x 5 + 3)cos x 2
2 x 2 5
6) y
Kuta Software - Infinite Calculus
Name_
Implicit Differentiation
Date_ Period_
For each problem, use implicit differentiation to find
dy
in terms of x and y.
dx
1) 2 x 3 = 2 y 2 + 5
2) 3 x 2 + 3 y 2 = 2
3) 5 y 2 = 2 x 3 5 y
4) 4 x 2 = 2 y 3 + 4 y
5) 5 x 3
Kuta Software - Infinite Calculus
Name_
Differentiation - Chain Rule
Date_ Period_
Differentiate each function with respect to x.
1) y = ( x 3 + 3)
5
3) y = (5 x 3 3)
2) y = (3 x 5 + 1)
3
4) y = (5 x 2 + 3)
4
5) f ( x) =
4
3 x 4 2
6) f ( x) =
7) f ( x) =
Kuta Software - Infinite Calculus
Name_
Differentiation - Product Rule
Date_ Period_
Differentiate each function with respect to x.
1) y = x 3 (3 x 4 2)
2) f ( x) = x 2 (3 x 2 2)
3) y = (2 x 4 3)(2 x 2 + 1)
4) f ( x) = (2 x 4 3)( x 2 + 1)
5) f ( x) = (5 x
Kuta Software - Infinite Calculus
Name_
Higher Order Derivatives
Date_ Period_
For each problem, find the indicated derivative with respect to x.
1) y = x 2
Find
d 2y
dx 2
2) f ( x) = 4 x 3
Find f '
3) y = 4 x
d 3y
Find 3
dx
4) f ( x) = 5 x 4
Find f '
5)
Kuta Software - Infinite Calculus
Name_
Newton's Method
Date_ Period_
Use two iterations of Newton's Method to approximate the real zeros of each function. Use the provided
initial guess.
2) y = x 5 2 x 3 + x 4
Guess: 1.8
1) y = cos 3 x 3 x
Guess: 0.4
y
y
Kuta Software - Infinite Calculus
Name_
Differentials
Date_ Period_
For each problem, find the differential dy.
1) y = x 3 2
2) y =
3
x
For each problem, find the general formulas for dy and y.
3) y = x 3 2
4) y =
2
x
For each problem, find dy and y, giv
Kuta Software - Infinite Calculus
Name_
Derivatives of Inverse Functions
For each problem, find ( f
)' ( x) by direct computation.
1
1) f ( x) = 3 x + 3
For each problem, find ( f
Date_ Period_
2) f ( x) = 2 x + 3
)' ( x) by using the theorem ( f 1)' ( x)
Kuta Software - Infinite Calculus
Name_
Differentiation Rules, with Tables
Date_ Period_
For each problem, you are given a table containing some values of differentiable functions f ( x), g( x) and
their derivatives. Use the table data and the rules of di